Mrs Rinehart's two eldest children, as well as former business partners of her late mining pioneer father Lang Hancock, are fighting for multibillion-dollar stakes in a lucrative iron ore project that's half owned by Rio Tinto.
The complex case that started on Monday centres on a claim by Wright Prospecting, the family company of Mr Hancock's former business partner Peter Wright.
It has demanded a half share in a Hope Downs mine and royalties based on a series of partnership agreements between the men's companies over three decades.
Deceased prospector Don Rhodes' family company DFD Rhodes is also involved, claiming a 1.25 per cent royalty share of Hope Downs' production.
Mrs Rinehart is executive chair of Hancock Prospecting, and her son John Hancock and daughter Bianca Rinehart claim they are entitled to half of its share in the massive Hope Downs operation, assets their grandfather allegedly left them.
More than a dozen lawyers representing the parties packed the Perth courtroom, with lawyers for Wright Prospecting opening proceedings about 13 years after the case started.
They gave Justice Jennifer Smith a detailed history of the business partnership and the iron ore-rich land where the Hope Downs mine is now located.
"This case turns in large measure on the proper construction of the partnership agreement," Grant Donaldson SC said.
"Relevant to these proceedings is the obligation to act in the best interest of the partnership."
The trial is expected to run until November, with any judgment potentially superseded by the looming outcome of Federal Court arbitration between Hancock Prospecting and Mrs Rinehart's children concerning the same issues.
Mrs Rinehart was dealt a blow last week when the Supreme Court rejected her bid to have thousands of pages of evidence likely to be presented at the trial classified as confidential.
The documents, which contain claims about Mrs Rinehart's alleged conduct, could have resulted in the court being closed for much of the trial had the application succeeded.
Mrs Rinehart inherited her father's iron ore discovery in WA's Pilbara region and then forged a mining empire after he died in 1992.
She developed mines from the tenements Mr Hancock and Mr Wright discovered at Hope Downs in the 1950s with Rio Tinto, which has a 50 per cent stake in the project.
This was followed by Hancock Prospecting's flagship project, the Roy Hill iron ore mine.
Her wealth, estimated to be about $36 billion, has been bitterly contested.
She spent years in courts fighting her stepmother Rose Porteous over the fortune after Mr Hancock died.
Mrs Rinehart's ongoing battle with her children over the family trust resulted in her being granted control in 2015.
The Hope Downs iron ore mining complex is made up of four open-pit mines near Newman.
It produces more than 45 million tonnes each year and is one of Australia's largest and most successful iron ore projects.
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